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Power Domain Constructions
 SCIENCE OF COMPUTER PROGRAMMING
, 1998
"... The variety of power domain constructions proposed in the literature is put into a general algebraic framework. Power constructions are considered algebras on a higher level: for every ground domain, there is a power domain whose algebraic structure is specified by means of axioms concerning the alg ..."
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Cited by 23 (9 self)
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The variety of power domain constructions proposed in the literature is put into a general algebraic framework. Power constructions are considered algebras on a higher level: for every ground domain, there is a power domain whose algebraic structure is specified by means of axioms concerning the algebraic properties of the basic operations empty set, union, singleton, and extension of functions. A host of derived operations is introduced and investigated algebraically. Every power construction is shown to be equipped with a characteristic semiring such that the resulting power domains become semiring modules. Power homomorphisms are introduced as a means to relate different power constructions. They also allow to define the notion of initial and final constructions for a fixed characteristic semiring. Such initial and final constructions are shown to exist for every semiring, and their basic properties are derived. Finally, the known power constructions are put into the general framewo...
Lower Bag Domains
 Fundamenta Informaticae
, 1995
"... . Two lower bag domain constructions are introduced: the initial construction which gives free lower monoids, and the final construction which is defined explicitly in terms of second order functions. The latter is analyzed closely. For sober dcpo's, the elements of the final lower bag domains can b ..."
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Cited by 7 (3 self)
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. Two lower bag domain constructions are introduced: the initial construction which gives free lower monoids, and the final construction which is defined explicitly in terms of second order functions. The latter is analyzed closely. For sober dcpo's, the elements of the final lower bag domains can be described concretely as bags. For continuous domains, initial and final lower bag domains coincide. They are continuous again and can be described via a basis which is constructed from a basis of the argument domain. The lower bag domain construction preserves algebraicity and the properties I and M, but does not preserve bounded completeness, property L, or bifiniteness. 1 Introduction Power domain constructions [13, 15, 16] were introduced to describe the denotational semantics of nondeterministic programming languages. A power domain construction is a domain constructor P , which maps domains to domains, together with some families of continuous operations. If X is the semantic domain ...
Directions in Functional Programming for Real(Time) Applications
 In the International Workshop on Embedded Software (ES
, 2001
"... . We review the basics of functional programming, and give a brief introduction to emerging techniques and approaches relevant to building realtime software. In doing so we attempt to explain the relevance of functional programming concepts to the realtime applications domain. In particular, w ..."
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Cited by 7 (3 self)
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. We review the basics of functional programming, and give a brief introduction to emerging techniques and approaches relevant to building realtime software. In doing so we attempt to explain the relevance of functional programming concepts to the realtime applications domain. In particular, we address the use of types to classify properties of realtime computations. "If thought corrupts language, language can also corrupt thought." George Orwell, Politics and the English Language 1
Semantics of Binary Choice Constructs
"... This paper is a summary of the following six publications: (1) Stable Power Domains [Hec94d] (2) Product Operations in Strong Monads [Hec93b] (3) Power Domains Supporting Recursion and Failure [Hec92] (4) Lower Bag Domains [Hec94a] (5) Probabilistic Domains [Hec94b] (6) Probabilistic Power Domains, ..."
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This paper is a summary of the following six publications: (1) Stable Power Domains [Hec94d] (2) Product Operations in Strong Monads [Hec93b] (3) Power Domains Supporting Recursion and Failure [Hec92] (4) Lower Bag Domains [Hec94a] (5) Probabilistic Domains [Hec94b] (6) Probabilistic Power Domains, Information Systems, and Locales [Hec94c] After a general introduction in Section 0, the main results of these six publications are summarized in Sections 1 through 6. 0 Introduction In this section, we provide a common framework for the summarized papers. In Subsection 0.1, Moggi's approach to specify denotational semantics by means of strong monads is introduced. In Subsection 0.2, we specialize this approach to languages with a binary choice construct. Strong monads can be obtained in at least two ways: as free constructions w.r.t. algebraic theories (Subsection 0.3), and by using second order functions (Subsection 0.4). Finally, formal definitions of those concepts which are used in all...
A Little Synopsis on Streams, Stream Processing Functions, and StateBased Stream Processing
"... Abstract Specification of interactive distributed systems has been a challenge for decades. We present an overview of the specification techniques for these systems based on dataflow networks and stream processing. It covers models of streams and specification of stream processing systems that are r ..."
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Abstract Specification of interactive distributed systems has been a challenge for decades. We present an overview of the specification techniques for these systems based on dataflow networks and stream processing. It covers models of streams and specification of stream processing systems that are related to and based on the development method Focus invented by Manfred Broy and his group. We introduce a basic set of manipulator operations for streams, stream bundles, stream processing functions, and give a summary of related statebased specification techniques. Furthermore we sketch an overview of implementations for the Focus framework. These range from formalizations using interactive proof assistants and model checkers to the modeling IDE AutoFocus.